I don't think the issues are as cut and dry as you make them seem.
I'd be willing to bet many of the prostitutes who are providing their services illegally would never be able to do so legally - as much more desirable people would begin to offer competing services.
Believe it or not, many people also choose to be homeless; whether or not this is a result of another issue like drugs or mental illness is irrelevant. Many mentally ill people would rather deal with the disease than the treatment.
No doubt we could do more to aid societies issues, but it's unlikely that we'll ever fully resolve many of them.
No doubt we could do more to aid societies issues, but it's unlikely that we'll ever fully resolve many of them.